document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=627346>Question 627346</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the least value of:- <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+sec%5E2%28x%29+%2B+9+cosec%5E2%28x%29 ALIGN=MIDDLE  ALT=\"4+sec%5E2%28x%29+%2B+9+cosec%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394891 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=394891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sec%5E2%28x%29+%2B+9cosec%5E2%28x%29 ALIGN=MIDDLE  ALT=\"4sec%5E2%28x%29+%2B+9cosec%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282sec%28x%29+-+3cosec%28x%29%29%5E2+%2B+12sec%28x%29cosec%28x%29 ALIGN=MIDDLE  ALT=\"%282sec%28x%29+-+3cosec%28x%29%29%5E2+%2B+12sec%28x%29cosec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The minimum value of the expression will be obtained when the square term will be zero.<BR>\n" );
document.write( "To satisfy that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sec%28x%29+=+3cosec%28x%29 ALIGN=MIDDLE  ALT=\"2sec%28x%29+=+3cosec%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Thus, the expression reduces to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8sec%5E2%28x%29 ALIGN=MIDDLE  ALT=\"8sec%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This will be minimum when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sec%5E2%28x%29 ALIGN=MIDDLE  ALT=\"sec%5E2%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be minimum which is 1.\r<BR>\n" );
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document.write( "Hence, the minimum value of the given expression is 8. </SPAN>\n" );
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